Let's solve this step-by-step.

1. Define Variables:

   • Let $PQ = a$, $QR = b$, and $PR = c$ (hypotenuse of the triangle).

2. Use Perimeter Information:

   • The perimeter of $\triangle PQR$ is given as 126 cm: $a + b + c = 126$

3. Use Area Information:

   • The area of $\triangle PQR$ is given as 630 square cm. Since $\triangle PQR$ is a right triangle with $Q$ as the right angle, the area can be calculated as: $\frac{1}{2} \cdot a \cdot b = 630$
   • Multiplying both sides by 2, we get: $a \cdot b = 1260$

4. Use Pythagoras' Theorem:

   • In a right triangle, $c^2 = a^2 + b^2$.

5. Express $b$ in Terms of $a$ and Substitute:

   • From the perimeter equation, $b = 126 - a - c$.
   • Using $c^2 = a^2 + b^2$ along with ( a \cdot b